On the cooperation of interval-valued fuzzy sets and genetic tuning to improve the performance of fuzzy decision trees

Fuzzy decision trees are widely employed to face classification problems since they combine the high interpretability given by the decision tree and the capability of management of the uncertainty inherent to fuzzy logic. However, the success of fuzzy systems in general depends, to a large degree, on the choice of the membership functions. For this reason, we propose to model the linguistic labels by means of Interval-Valued Fuzzy Sets to take into account the ignorance related to their definition. On the other hand, we define an evolutionary method to tune the shape of the Interval-Valued Fuzzy Sets looking for the best ignorance degree that each Interval-Valued Fuzzy Set represents. In this contribution, we will make use of the fuzzy ID3 algorithm as a base technique from which to apply our methodology. The experimental study shows how our methodology enhances the performance of the base fuzzy decision tree. Furthermore, we compare our approach with respect to four state-of-the-art fuzzy decision trees and C4.5 as a representative algorithm for crisp decision trees. The goodness of our proposal is tested on a large collection of data-sets and it is supported by an exhaustive statistical analysis.